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No trigonometry, no algebra (Posted on 2005-12-23) Difficulty: 3 of 5
Look at the drawing below, where AB = BC = CD = DT = h, and TD perpendicular to AD:
                                   
                                   o T
                                   |
                                   | (h) 
                                   |
                                   |
  +----------+----------+----------o 
  A    (h)   B    (h)   C    (h)   D
The line AT makes an angle x with AD; the line BT makes an angle y with BD; the line CT makes an angle z with CD.

Using only geometry, prove that (angle x) + (angle y) = (angle z).

See The Solution Submitted by pcbouhid    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts With Trig. Identity | Comment 5 of 10 |
 
                                      1     1
                                     --- + ---
               tan(x) + tan(y)        3     2
  tan(x+y) = ------------------- = ------------- = 1 = tan(z)
              1 - tan(x)*tan(y)          1   1
                                    1 - ---x---
                                         3   2
Therefore, z = x+y

 


  Posted by Bractals on 2005-12-24 03:41:34
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